Optical modulators of interest in the present invention are integrated optical waveguide structures which may be considered as having an input section, a central phase modulating interferometer (IF) section and an output section. The input and output sections may be either Y-junction (YJ) optical waveguide structures (YJ splitter with one input waveguide dividing into two output waveguides or YJ combiner wherein two input waveguides merge into a single output waveguide) or optical directional couplers (DC) which are 2.times.2 optical ports having paired coupled waveguides. One type of optical modulator of interest is the Mach-Zehnder (MZ) modulator. This has a YJ splitter input section, a central IF section and a YJ combiner output (YJ-IF-YJ in our notation). Another type of optical modulator of interest is the balanced bridge modulator (BBI). This has three possible configurations: (1) YJ-IF-DC, (2) DC-IF-YJ or (3) DC-IF-DC. Note that at least one of the end sections is always a DC section. Another way of characterizing these devices is in terms of the number of input and output waveguide ports, i.e. the MZ is 1.times.1, the BBI is 1.times.2, or 2.times.1, or 2.times.2. For a 2.times.2 BBI both input ports can be used or one input port may be unused effectively utilizing the device in a 1.times.2 mode of operation.
In prior art, two modulators have been connected both in series or in parallel, in an effort to improve linearity of the light power vs. modulating voltage transfer characteristic over a wide bandwidth operation range. In the dual parallel schemes, the outputs of two modulators are combined either incoherently or coherently or two orthogonal polarizations of the same modulator structure are combined to serve as the equivalents of two different parallel modulators. FIG. 1 shows a dual parallel modulator with YJs 21, bias electrodes 23, RF electrodes 25 and a phase modulator 27.
In the parallel connection scheme the two modulators (or the two orthogonal polarizations of a single modulator) are generally driven with different drive voltages or are designed to have different modulating efficiencies, often achieved through the use of different electrode lengths, and are fed with different optical powers, such that the net result is to subtract the nonlinear distortion terms generated in the two modulators. Unfortunately, this occurs at the expense of the desired linear drive signals being partially cancelled. In addition, such schemes yield a higher optical loss and require a higher RF drive power. Other problems have to do with the electrical and acoustical cross-talk between the two sections which, because of the parallel layout, are in close proximity to one another and are oriented broadside with respect to acoustic radiation coupling.
In the serial connection schemes, directional couplers with sub-sections are used with electrodes connected to several sub-sections. In these implementations, the modulating signal, typically a radio frequency (RF) drive, is applied to one electrode sub-section only and the other sub-sections are either un-modulated or DC biased.
In a paper entitled "Linearization of Electro-Optic Modulators by a Cascade Coupling of Phase Modulating Electrodes" by H. Skeie and R. V. Johnson, published in SPIE, Vol. 1583, Integrated Optical Circuits (1991), p. 153-164 the authors disclose parallel and cascade coupling of two modulators. FIG. 2 shows structures illustrated in the paper where FIG. 2a is a tandem MZ configuration with a first input YJ 31, a bias electrode 33, a first IF 35 and a first YJ output 37 joined to a second input YJ 32, a second bias electrode 34 and IF 36 and a second output YJ 38. In FIG. 2b, a MZ modulator 41, similar to the first MZ of FIG. 2a is connected through a bias electrode 43, an IF 45 to an output YJ 47. The second modulator formed by DC 48, bias electrode 42, IF 44 and YJ 46 is a BBI used in a 1.times.1 fashion. FIG. 2c shows a MZ modulator 51 coupled to a BBI modulator 53 as in FIG. 2b, except that the output section 55 is a DC. Lastly, the authors disclose in FIG. 2d a BBI modulator 61 coupled to another BBI modulator 63 and they note that the second stage is identical to the first.
Modulator L-V transfer characteristic--linearity and distortion specifications
Modulator linearity and the residual nonlinear distortion are specified in terms of the harmonic response of the power series expansion of the L-V (Light power vs. modulation Voltage) transfer characteristic. The background material reviewed here sets the mathematical notation and is well known prior art with the exception of the normalizations of power series coefficients introduced for meaningful comparison criteria among different devices.
Any electro-optic modulator (FIG. 3) can be described as a system with an optical input port where typically un-modulated CW light power P.sub.in is injected, an optical output where modulated optical power P.sub.o (t) is collected, and an electrical modulating port where a modulating voltage signal .nu.(t) is applied. The L-V characteristic is a relation between these three quantities, with P.sub.in considered a parameter: EQU P.sub.o (v)=P.sub.in Q(v) (1)
The output power is linear in the input power but is generally nonlinear in the modulating voltage, and it is our objective to reduce this nonlinearity.
The power series expansion of the transfer characteristic (Eq. 1) can be expressed as EQU P.sub.o =P(1+d.sub.1 .phi.+d.sub.2 .phi..sup.2 +d.sub.3 .phi..sup.3 + . . . ) (2)
where .phi. is a normalized voltage expressing the interferometric phase retardation ##EQU1## .nu. is the modulating voltage applied to the interferometer electrodes, V.sub..pi. is a constant called half-wave voltage--the voltage required to produce .pi. phase change in .phi. ##EQU2## P is the average output optical power, P.sub.in is the input optical power, and 10 log.sub.10 (.LAMBDA.) represents the device optical insertion loss in dB. In this disclosure, the even and third order distortions are substantially nulled rendering the dominant distortion to be the residual fifth order one. The L-V characteristic expressed in a power series with only odd terms, starting with the fifth order one is, ##EQU3## where we introduced normalized optical intensity I(.phi.) as the ratio of optical power to average power.
Assume now that the modulation signal is a sum of sinusoidal tones ##EQU4## is the modulation index in radians.
Introduce the optical modulation index (OMI) m as the ratio of the peak optical power of each of the sinusoidal carriers (Pd.sub.1 .beta.) to the average optical power (P), ##EQU5##
For a given transmitted average power, it is the OMI that determines the carrier to noise ratio. To compare two systems with the same carrier to noise ratio in terms of their nonlinear distortions, one would drive both to the same OMI.
Using the formalism above it is possible to show that the ratio of the fifth order intermodulation term to the carrier is proportional to d.sub.5.sup.norm m.sup.4, where ##EQU6## is a normalized fifth order coefficient which can be used as a figure of merit to compare two different systems both driven to the same modulation index m in terms of the strengths of their fifth order intermodulation distortion.
For a given average optical power P the amplitude in the optical power domain of each of the carriers is given by ##EQU7##
Therefore it is advantageous to maximize the linear modulation coefficient d.sub.1 and reduce the drive voltage V.sub..pi. as well as increase the average optical power P by reducing the insertion loss .LAMBDA..
Mathematical description of optical two-ports
The directional coupler and the two-arm interferometer are optical two-port devices. A generic two-port integrated optical device is illustrated in FIG. 4. It can be mathematically described in terms of a two-port transfer matrix M relating the electric fields at the two waveguide input ports 65 and 67 with the electric fields at the two waveguide output ports 71 and 73: ##EQU8##
Directional coupler (DC)
Consider a directional coupler consisting of two closely spaced waveguides, generally with biasing electrodes. The well known coupled mode equations describe the evolution of the E-fields along a coupler and the exchange of energy between the two waveguides. Let .kappa. denote the coupling coefficient per unit length between the waveguides and .delta. denote the asynchronism coefficient which is proportional to the applied voltage and to the induced phase difference per unit length between the two coupler arms, ##EQU9## with R some proportionality constant. Throughout the document .DELTA..beta. and .delta. will be used somewhat interchangeably.
A coupler with .delta.=0 is called symmetric and a coupler with nonzero .delta. is called asymmetric. The asymmetry may be structural-unequal waveguides (differing in cross-sectional dimensions and/or refractive indexes) or for the so-called .DELTA..beta. coupler it may be an asymmetry induced by the applied voltage on the electrodes. The general solution to the coupled mode equations is represented in terms of a two-port transfer matrix C [.kappa..delta.] given by ##EQU10## wherein using the notation ##EQU11## the parameters.GAMMA.,.DELTA.,K,K are expressed as ##EQU12##
From Eq. 13 it is apparent that as the coupler is made more asymmetric e.g. by applying bias voltage and causing a .DELTA..beta. difference, the magnitude of the cross-over coefficient K diminishes according to a sin (.gamma.)/.gamma. function.
As a special case of the equations above, consider a symmetric coupler .delta.=0 for which .GAMMA.=.gamma.=.kappa.L, K=sin (.gamma.) and .DELTA.=0. In this case the coupler can be interchangeably described by its coupling ratio K or its coupling angle .gamma.. For the asymmetric .DELTA..beta. coupler, the coupling ratio is defined by the analogous coupling angle .GAMMA. but a full description of the coupler must consider the phase shift .DELTA. as well. Occasionally we also describe a coupler by its power cross-over ratio K.sup.2, e.g. a 50%/50% coupler.
Push-pull phase modulating interferometer matrix (IF)
An interferometer (IF) transfer matrix corresponds to pure phase shifts with no cross-coupling between the two waveguides ##EQU13## with .phi. the differential phase retardation between the two arms. Control of the device requires applying some static bias voltage V.sub.b to the interferometer electrodes, thus in the most general case of interferometer matrix is F[.phi.+.eta.] with ##EQU14## the static bias phase.
The objectives of the invention are the design of modulator devices and related bias and tuning systems to improve the following performance criteria:
1) reduce the nonlinearities over a broad frequency band. PA0 2) maximize the modulation efficiency i.e. maximize the linear modulation coefficient and minimize the half-wave drive voltage and the optical losses. PA0 3) attain the ability to electronically tune the device to the above optimum operating point in the wake of the inevitable process irregularities. PA0 A) Dual tandem and split tandem architectures with multiple electrical drives. PA0 B) Device broadband operation achieved by means of balanced splitting ratios i.e. dual electrical drives that are equal in magnitude and either in phase or 180.degree. out of phase. PA0 C) Choice of coupler coefficients which are optimal for the reduction of odd order distortions and simultaneously for the enhancement of the linear modulation coefficient. PA0 D) Usage of voltage-tunable .DELTA..beta. couplers (with the .DELTA..sub..kappa. couplers covered as a special case) to enhance the tunability of the couplers such that the device could be biased at its optimum operating regime. PA0 E) Application of bias voltages to the interferometer sections and to couplers by means of parametric feedback loops in order to null the even order distortions of the device as associated with .DELTA..beta. couplers while minimizing odd order distortions.